About: Geodesic manifold

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In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p.

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rdf:type	yago:WikicatManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Geodesic manifold (en) 측지선 완비 준 리만 다양체 (ko)
rdfs:comment	리만 기하학에서 측지선 완비 준 리만 다양체(測地線完備準Riemann多樣體, 영어: geodesically complete pseudo-Riemannian manifold)는 그 측지선들이 중간에 임의로 끊기지 않는 준 리만 다양체이다. (ko) In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p. (en)
dct:subject	Differential geometry Geodesic (mathematics) Manifolds Riemannian geometry
Wikipage page ID	6875557 (xsd:integer)
Wikipage revision ID	1076416440 (xsd:integer)
Link from a Wikipage to another Wikipage	Schwarzschild metric End (topology) Big Bang Homogeneous space Hopf–Rinow theorem Differential geometry Compact space Mathematics Geodesic (mathematics) General relativity Geodesic Connected space Clifton–Pohl torus Complete metric space Symmetric space Torus Manifolds Euclidean space Exponential map (Riemannian geometry) Pseudo-Riemannian manifold Riemannian manifold Riemannian metric Riemannian geometry Academic Press Sphere Penrose–Hawking singularity theorems
sameAs	Geodesic manifold Geodesic manifold Geodesic manifold Geodesic manifold Geodesic manifold
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Math dbt:Mvar dbt:Sub dbt:Manifolds
has abstract	In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p, you can follow a "straight" line indefinitely along any direction. More formally, the exponential map at point p, is defined on TpM, the entire tangent space at p. Equivalently, consider a maximal geodesic . Here is an open interval of , and, because geodesics are parameterized with "constant speed", it is uniquely defined up to transversality. Because is maximal, maps the ends of to points of ∂M, and the length of measures the distance between those points. A manifold is geodesically complete if for any such geodesic , we have that . (en) 리만 기하학에서 측지선 완비 준 리만 다양체(測地線完備準Riemann多樣體, 영어: geodesically complete pseudo-Riemannian manifold)는 그 측지선들이 중간에 임의로 끊기지 않는 준 리만 다양체이다. (ko)
prov:wasDerivedFrom	wikipedia-en:Geodesic_manifold?oldid=1076416440&ns=0
page length (characters) of wiki page	3249 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Geodesic_manifold
is Link from a Wikipage to another Wikipage of	Hopf–Rinow theorem Fréchet space Geodesic Complete metric space Gravitational singularity Shape of the universe Penrose–Hawking singularity theorems Geodesically complete Geodesically complete manifold
is Wikipage redirect of	Geodesically complete Geodesically complete manifold
is foaf:primaryTopic of	wikipedia-en:Geodesic_manifold

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